Nice, creative trip! By my calculation, via Flying Fish, that's 29,174 miles. I don't remember the exact number, but I thought they had limited the number of miles flown on RTW tickets - I'm not sure exactly, but I thought it was something like 28K?
After a search, I found my own answer here:
http://www.flyertalk.com/forum/north...ing-miles.html
It's 29K flown miles. Some other rules at the above link, too, for anyone who's thinking about booking it! In particular, post #7 by Bowgie.